آمار
| تعداد نشریات | 6 |
| تعداد شمارهها | 130 |
| تعداد مقالات | 1,624 |
| تعداد مشاهده مقاله | 1,871,761 |
| تعداد دریافت فایل اصل مقاله | 1,732,133 |
On leap Zagreb indices of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 3، دوره 2، شماره 2، آذر 2017، صفحه 99-117 اصل مقاله (451.56 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2017.25949.1059 | ||
| نویسندگان | ||
| Ivan Gutman* 1؛ Ahmed M Naji2؛ Nandappa D Soner3 | ||
| 1University of Kragujevac | ||
| 2Department of Mathematics, University of Mysore, Mysusu, India | ||
| 3Department of Mathematics, University of Mysore, Mysuru, India | ||
| چکیده | ||
| The first and second Zagreb indices of a graph are equal, respectively, to the sum of squares of the vertex degrees, and the sum of the products of the degrees of pairs of adjacent vertices. We now consider analogous graph invariants, based on the second degrees of vertices (number of their second neighbors), called leap Zagreb indices. A number of their basic properties is established. | ||
| کلیدواژهها | ||
| degree (of vertex)؛ Second degree؛ Zagreb indices؛ leap Zagreb indices | ||
| مراجع | ||
|
[1] A. Ashrafi, T. Došlić, and A. Hamzeh, The Zagreb coindices of graph operations, Discrete Appl. Math. 158 (2010), no. 15, 1571–1578.
[2] B. Basavanagoud and S. Patil, A note on hyper-Zagreb index of graph operations, Iran. J. Math. Chem. 7 (2016), no. 1, 89–92.
[3] B. Borovicanin, K.C. Das, B. Furtula, and I. Gutman, Bounds for Zagreb indices, MATCH Commun. Math. Comput. Chem 78 (2017), no. 1, 17–100.
[4] R.M. Damerell, On Moore graphs, Proc. Cambridge Phil. Soc. 74 (1973), no. 2, 227–236.
[5] K.C. Das and I. Gutman, Some properties of the second Zagreb index, MATCH Commun. Math. Comput. Chem 52 (2004), no. 1, 103–112.
[6] T. Došlić, Vertex-weighted Wiener polynomials for composite graphs, Ars Math. Contemp. 1 (2008), no. 1, 66–80.
[7] M. Eliasi, A. Iranmanesh, and I. Gutman, Multiplicative versions of first Zagreb index, MATCH Commun. Math. Comput. Chem. 68 (2012), no. 1, 217–230.
[8] B. Furtula, I. Gutman, and M. Dehmer, On structure-sensitivity of degree-based topological indices, Appl. Math. Comput. 219 (2013), no. 17, 8973–8978.
[9] I. Gutman, Multiplicative Zagreb indices of trees, Bull. Soc. Math. Banja Luka 18 (2011), 17–23.
[10] I. Gutman, Degree-based topological indices, Croat. Chem. Acta 86 (2013), no. 4, 351–361.
[11] I. Gutman and K.C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem 50 (2004), 83–92.
[12] I. Gutman, B. Furtula, K. Vukićević, and G. Popivoda, On Zagreb indices and coindices, MATCH Commun. Math. Comput. Chem 74 (2015), no. 1, 5–16.
[13] I. Gutman, B. Ruščić, N. Trinajstić, and C.F. Wilcox, Graph theory and molecular orbitals. XII. acyclic polyenes, J. Chem. Phys. 62 (1975), no. 9, 3399–3405.
[14] I. Gutman and N. Trinajstić, Graph theory and molecular orbitals. Total ϕelectron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972), no. 4, 535–538.
[15] F. Harary, Graph Theory, Addison-Wesley, Reading, 1969.
[16] A. Ilić and D. Stevanović, On comparing Zagreb indices, MATCH Commun. Math. Comput. Chem. 62 (2009), no. 3, 681–687.
[17] A. Ilić and B. Zhou, On reformulated Zagreb indices, Discrete Appl. Math. 160 (2012), no. 3, 204–209.
[18] M.H. Khalifeh, H. Yousefi-Azari, and A. Ashrafi, The first and second Zagreb indices of some graph operations, Discrete Appl. Math. 157 (2009), no. 4, 804–811.
[19] A. Miličević, S. Nikolić, and N. Trinajstić, On reformulated Zagreb indices, Mol. Diversity 8 (2004), no. 4, 393–399. [20] S. Nikolić, G. Kovačević, A. Miličević, and N. Trinajstić, The Zagreb indices 30 years after, Croat. Chem. Acta 76 (2003), no. 2, 113–124.
[21] K. Pattabiraman and M. Vijayaragavan, Hyper Zagreb indices and its coindices of graphs, Bull. Int. Math. Virt. Inst. 7 (2017), no. 1, 31–41.
[22] N.D. Soner and A.M. Naji, The k-distance neighborhood polynomial of a graph, Int. J. Math. Comput. Sci. WASET Conference Proceedings, San Francico, USA, Sep 26-27, 3 (2016), no. 9, part XV, 2359–2364.
[23] K. Xu and K.C. Das, Trees, unicyclic, and bicyclic graphs extremal with respect to multiplicative sum Zagreb index, MATCH Commun. Math. Comput. Chem. 68 (2012), no. 1, 257–272.
[24] K. Xu, K.C. Das, and K. Tang, On the multiplicative Zagreb coindex of graphs, Opuscula Math. 33 (2013), no. 1, 191–204.
[25] K. Xu and H. Hua, A unified approach to extremal multiplicative Zagreb indices for trees, unicyclic and bicyclic graphs, MATCH Commun. Math. Comput. Chem. 68 (2012), no. 1, 241–256.
[26] S. Yamaguchi, Estimating the Zagreb indices and the spectral radius of triangleand quadrangle-free connected graphs, Chem. Phys. Lett. 458 (2008), no. 4, 396–398. | ||
|
آمار تعداد مشاهده مقاله: 2,488 تعداد دریافت فایل اصل مقاله: 3,537 |
||